Intermolecular vibrations of (CH2)2O–HF and –DF hydrogen bonded complexes investigated by Fourier transform infrared spectroscopy and ab initio calculations

Physical Chemistry Chemical Physics c004100a

IntermolecularQ1 vibrations of (CH2)2O–HF and –DF

hydrogen bonded complexes investigated by Fourier

transform infrared spectroscopy and ab initiocalculations

M. Cirtog, P. Asselin,* P. Soulard, B. Madebene andM. E. Alikhani

The vibrational spectrum of the intermolecular stretchingO� � �H (ns) mode of (CH2)2O� � �HF reveals inter-intermolecular anharmonic couplings between ns and lowfrequency bending modes (nd1,2).

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IntermolecularQ1 vibrations of (CH2)2O–HF and –DF hydrogen bonded

complexes investigated by Fourier transform infrared spectroscopy

and ab initio calculations

M. Cirtog,ab

P. Asselin,*ab

P. Soulard,ab

B. Madebeneab

and M. E. Alikhaniab

Received 9th March 2010, Accepted 16th June 2010

DOI: 10.1039/c004100a

A series of Fourier transform infrared spectra (FTIR) of the hydrogen bonded complexes

(CH2)2O–HF and –DF have been recorded in the 50–750 cm�1 range up to 0.1 cm�1 resolution in

a static cell maintained at near room temperature. The direct observation of three intermolecular

transitions enabled us to perform band contour analysis of congested cell spectra and to

determine reliable rovibrational parameters such as intermolecular frequencies, rovibrational

and anharmonic coupling constants involving two l1 and l2 librations and one s stretching

intermolecular motion. Inter-inter anharmonic couplings could be identified between nl1, nl2, nsand the two lowest frequency bending modes. The positive sign of coupling constants

(opposite with respect to acid stretching intra-inter ones) reveals a weakening of the hydrogen

bond upon intermolecular excitation. The four rovibrational parameters ns and xsj (j = s, d1, d2)derived in the present far-infrared study and also in a previous mid-infrared one [Phys. Chem.

Chem. Phys. 2005, 1, 592] make deviations appear smaller than 1% for frequencies and 12% for

coupling constants which gives confidence to the reliability of the data obtained. Anharmonic

frequencies obtained at the MP2 level with Aug-cc-pvTZ basis set agree well with experimental

values over a large set of frequencies and coupling constants. An estimated anharmonic corrected

value of the dissociation energy DCP0 for both oxirane–HF (2424 cm�1) and –DF (2566 cm�1) has

been derived using a level of theory as high as CCSD(T)/Aug-cc-pvQZ, refining the harmonic

value previously calculated for oxirane–HF with the MP2 method and a smaller basis set. Finally,

contrary to short predissociation lifetimes evidenced for acid stretching excited states, any

homogeneous broadening related to vibrational dynamics of (CH2)2O–HF and –DF has been

observed within the three highest frequency intermolecular states, as expected with low excitation

energies largely below the dissociation limit as well as a negligible IVR contribution.

I. Introduction

Hydrogen bonded complexes are important prototypes for

investigating weak inter- and intramolecular forces in a large

variety of chemical phenomena from the condensed matter to

the gas phase.1–5 The development of high resolution laser and

FTIR spectroscopic techniques combined with supersonic jet

environments has contributed to extend structural studies in

the ground vibrational state, from microwave spectroscopy,

to include vibrationally excited states of molecular

complexes.6–13 Vibrational dynamics has also been investi-

gated which evidenced mode specific lifetimes over large

temporal scales, depending on the nature of the excited mode:

either intramolecular mode or intermolecular stretching and

bending directly influenced by intramolecular vibrational

relaxation and vibrational predissociation phenomena.14–20

High resolution spectroscopy of hydrogen bonded dimers

is a particularly relevant technique to provide accurate inter-

molecular potential energy surfaces (IPES) for pairwise

interactions provided that the rovibrational spectrum

of a wide variety of transitions labelled as jv00 intra; v00inter;1;v00 inter;2; . . .i ! jv0 intra; v0 inter;1; v0 inter;2; . . .i where v00intra, v

00inter;i,

v0 intra and v0 inter;i are the quantum numbers for one intra- and i

intermolecular modes in ground and excited states, respectively,

could be observed and analysed: in particular, fundamentals

(|0,0,. . .i- |vintra,0,. . .i and |0,0,. . .i- |0,vintra,1,. . .i), combi-

nation sum bands (|0,0,. . .i - |vintra,vinter,1,. . .i), overtones

(|0,0,. . .i - |nvintra,0,. . .i) and hot transitions (|0,vinter,1,. . .i -|vintra,vinter,1,. . .i). Unlike transitions involving intramole-

cular vibrations, pure intermolecular transitions such as

|0,0,vinter,2,. . .i - |0,vinter,1,vinter,2,. . .i depend only on the

properties of the IPES. Therefore direct observation and

rovibrational analysis of rotationally resolved absorption

spectra of intermolecular vibrations of gas phase bimolecular

complexes remains an exciting challenge to obtain accurate

probes of the intermolecular potential. Due to the lack

of tunability of laser sources or to the poor brightness of

thermal laboratory sources in the far infrared range (FIR)

combined with the generally few intense intermolecular

vibrations, few studies have been reported until now.21–30

Using the technique termed ‘‘intracavity FIR laser electric

resonance spectroscopy’’ Saykally’s group performed high

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aUPMC Univ. Paris 06, UMR 7075, Laboratoire de Dynamique,Interactions et Reactivite (LADIR), F-75005, Paris, FranceQ2

b CNRS, UMR 7075, Laboratoire de Dynamique, Interactions etReactivite (LADIR), F-75005, Paris, France

This journal is �c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 1–9 | 1

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

resolution laser measurements of vibration–rotation-tunnel-

ling (VRT) spectroscopy on low frequency van der Waals

vibrations in regions located here and there the barrier to

internalQ3 motion on the IPES.22 Precise intermolecular poten-

tials have also been obtained with prototype systems for 2-D

(Ar–HCl, Ar–HF)23,24 and 3-D (Ar–H2O) VRT dynamics25

but the sensitivity of these laser-based methods becomes

insufficient above 100 cm�1. More recently, Nelander

et al.26,27 recorded several spectra of intermolecular stretching

and libration bands related to weakly bound small dimers

(NH3–HCN, HCN–HCl. . .) by means of high resolution static

gas Fourier transform far infrared spectroscopy around 200 K

interfaced to the infrared beamline of synchrotron radiation

from the electron storage ring MAX-1. From the precise

determination of rotational and centrifugal distortion

constants, the extent to which the excitation of intermolecular

librations destabilizes the hydrogen bond could be quantified.

Lastly, combining direct FTIR absorption and Raman

scattering techniques in the FIR range with supersonic

expansions, Suhm et al.28–30 provided reliable dynamical

information about intermolecular vibrations of several

hydrogen-bonded clusters of different sizes.

Nevertheless, the investigation of large molecular complexes

in the 100–700 cm�1 range which should ideally combine gas

phase devices such as supersonic jets for attaining low

rotational temperatures and spectroscopic techniques with

improved experimental sensitivity and large spectral coverage

remains challenging, in particular when high resolution is

necessary.

For several years our group extensively studied medium

strength hydrogen bonded one to one complexes between

organic bases and hydracids using standard absorption

interferometric techniques.31–35 Band contour simulations of

multi-temperature FTIR spectra carried out either in a super-

sonic free jet or a static cooled cell enabled the extraction of

sets of (ro)vibrational parameters in the intramolecular vHX = 1

state (hereafter designated ns) and to propose convincing

scenarios for the anharmonic vibrational couplings between

ns and the three lowest frequency intermolecular modes

(in plane (nd1) and out-of-plane (nd2) bend, hydrogen bond

stretch (ns)). Theoretical methods based on perturbative and

variational approaches for the treatment of coupled vibrations

reproduce well our experimental data.

Such infrared studies are efficient for probing the vibrational

behavior of the HX group, the most perturbed by the forma-

tion of the hydrogen bond. In this case a large redshift of the nsmode with respect to the HX monomer is generally observed,

as well as a strong increase of the intensity for the donor

stretch ns band. At the same time rovibrational information

relative to intermolecular modes is obtained indirectly , via

the observation of two-quanta hot transitions |0,vinter,i,. . .i-|vintra,vinter,i,. . .i or combination sum bands |0,0,. . .i -

|vintra,vinter,i,. . .i.In a previous paper, we had realized an extensive study of

(CH2)2O–HF and –DF hydrogen bonded complexes in the

donor stretch ns band region of HF (3400 cm�1) and DF

(2500 cm�1).33 The frequencies of three intermolecular modes

had been estimated from two-quanta transitions, anharmonic

constants and a lower bound of the predissociation lifetime for

HF and DF containing (CH2)2O had been obtained from the

band contour analysis of multi-temperature FTIR spectra. In

this paper we present new results about both systems which

have been reinvestigated in the 50–750 cm�1 range in order to

search spectral signatures of the five intermolecular modes. In

this spectral range the insufficient sensitivity of the LADIR

low pressure jet device practically prevents the exploitation

absorption signals related to these intermolecular modes.

New experimental data concerning symmetric nl1 and

asymmetric nl2 librations as well as the ns stretching hydrogen

bond mode are almost all obtained from congested near room

temperature cell-FTIR spectra. Band contours which result

from the superposition of rovibrational hot transitions

(low frequency initial levels populated at cell temperatures)

could be analyzed and provide complementary rovibrational

parameters to mid-infrared results. Comparison between

intermolecular data derived from FTIR spectra in the FIR

(|0,0,vinter,2,. . .i - |0,vinter,1,vinter,2,. . .i transitions) and MIR

ranges (|0,vinter,i,. . .i - |vintra,vinter,i,. . .i and |0,0,. . .i -

|vintra,vinter,i,. . .i transitions) as well as from anharmonic

ab initio calculations is discussed.

II. Experimental and computational details

Our supersonic jet-FTIR spectrometer has been described

in detail in previous studies. For taking into account the

reactivity of (CH2)2O with HF we reused the continuous

coaxial mixing nozzle that we developed especially for the

study of thiirane–hydracid complexes.31,32 This arrangement

allows the separate introduction of the reactive components up

to a few mm before the supersonic expansion and thereby

minimizes the possibility of reaction. The complexes are then

probed in a 16-pass multireflection arrangement by the IR

beam of a Bruker IFS 120 HR interferometer. The sensitivity

limits of our low pressure jet device has been reached to detect

intermolecular librations nl1 and nl2 of HF and DF bonded to

(CH2)2O, about ten times less intense than ns (ab initio

estimation for (CH2)2O–HF). Typical jet-FTIR spectra are

the Fourier transform of 500 coadded interferograms recorded

at 0.5 and 1 cm�1 resolution. As a result of the poor signal-to-

noise, jet spectra just served to estimate the band center of one

cold libration transition.

Cell spectra have been recorded in the 50–750 cm�1 region

at 0.1 and 0.5 cm�1 resolution between 253 and 293 K with

the 85 cm static cooled cell described elsewhere. Due to the

slow ring opening of oxirane in the presence of H(D)F36

the mixing of both components is carried out at low tempera-

tures. The disappearance of spectral features assigned to

(CH2)2O–H(D)F speeds up above 260 K making periodic

cycles of cell pumping and filling up of fresh gas mixture

necessary.

Two detectors have been used for covering the spectral

range of intermolecular modes: a silicon bolometer (from

Infrared Laboratories) operating at 4.2 K equipped with 100

and 600 cm�1 cut-on optical filters and a HgCdTe detector

combined with an external 1000 cm�1 cut-off filter. Oxirane

from Aldrich (99.5% purity) and HF from Messer Griesheim

(electronic quality) have been used without further purifica-

tion. DF is synthesized via recrystallization of KHF2 from

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2 | Phys. Chem. Chem. Phys., 2010, 12, 1–9 This journal is �c the Owner Societies 2010

D2O followed by thermal decomposition with an isotopic

purity of 90%.

All second-order Møller–Plesset (MP2) calculations

(geometries optimisation, harmonic and anharmonic

frequency calculations, and the correction for the basis set

superposition error) were carried out using the Gaussian03

package.37 All coupled-cluster (CCSD(T)) calculations

(geometries optimisation, harmonic frequencies calculations,

BSSE correction) were carried out using the Molpro2008

package.38 Dunning and co-workers augmented correlation

consistent basis set (Aug-cc-pvXZ, X = D, T, Q) were used

with both levels of theory.39

III. Results and discussion

III.1 Ab initio calculations

a Energetic and structural properties. Fig. 1 displays the

optimized structural parameters for the most stable form of

the oxirane–HF complex obtained at various levels of theory.

As shown in previous studies,33,40 the complex is of Cs

symmetry with the hydrogen atom of the acid pointing at

the oxygen of the base. The use of a larger basis set and a

higher correlated method does not significantly change the

structural parameters compared to those previously

obtained.33,40

Dissociation energy corrected from BSSE, DCPe and

corrected from harmonic zero point energy, DCP0 , are found

to be 3573 cm�1 (2750 cm�1), 3389 cm�1 (2567 cm�1) and 3319

cm�1 (2556 cm�1), respectively, at the MP2/Aug-cc-pvTZ,

MP2/Aug-cc-pvQZ and CCSD(T)/Aug-cc-pvTZ levels of

theory for the oxirane–HF complex.

When going to a higher correlated method than MP2 and

CCSD(T), DCPe decreases by 264 cm�1 and DCP

0 by 194 cm�1,

with the same basis set. This shows that MP2 overestimates

the strength of the hydrogen bond.

We note that the effect of the basis set size is not negligible.

Even though the Aug-cc-pvTZ is often considered as enough

large for studying the hydrogen bonded complexes, increasing

the basis set from the triple-zeta (Aug-cc-pvTZ) basis set to the

quadruple-zeta one (Aug-cc-pvQZ) significantly decreases the

values of DCPe and DCP

0 (respectively by 184 cm�1 and

183 cm�1) with MP2 method. Unfortunately, computer

limitations do not allow the optimisation and frequency

calculations at the CCSD(T)/Aug-cc-pvQZ level. However,

we assume that the energy shift for triple zeta would be of the

same order of magnitude as for MP2. Consequently the

following values DCPe E 3129 cm�1 and DCP

0 E 2373 cm�1

are found with the CCSD(T)/Aug-cc-pvQZ approach.

Finally, the use of anharmonic zero point energy correction

instead of harmonic at the MP2/Aug-cc-pvTZ level increases

the dissociation energy by 51 cm�1 leading to DCP0 =

2801 cm�1. Assuming the anharmonic correction would be

of the same order at the CCSD(T) level as for MP2, we

propose an estimated anharmonic corrected value DCP0 =

2424 cm�1 for the CCSD(T)/Aug-cc-pvQZ method. The same

procedure applied to the oxirane–DF complex leads to an

estimated anharmonic DCP0 value of 2566 cm�1 at CCSD(T)/

Aug-cc-pvQZ.

b Vibrational properties. The exact theoretical matching of

experimental vibrational frequencies is a hard task.

Nevertheless, ab initio calculations should reproduce well the

correct ordering and good isotopic frequency shifts to help in

assigning experimental infra-red bands. In order to investigate

the effect of the theory level on the calculated frequencies of

the oxirane–HF complex, we report in Table 1 harmonic

frequencies of the complex calculated with various basis set

(double, triple or quadruple zeta) for two correlated

approaches, MP2 and CCSD(T). The frequency mode

assignments of the base in the complex are taken from the

study of the oxirane monomer in C2v symmetry. Other

frequencies, reported in bold character, are the five inter-

molecular vibrational modes and the acid stretching. MP2/

Aug-cc-pvQZ harmonic frequencies of both monomers are

also reported.

A deep analysis of the theoretical study of the vibrational

modes shows that we have to pay particular attention to four

points:

(1) For both MP2 and CCSD(T) methods, we note that the

calculated frequencies and infrared intensities do not depend

on the basis set size (triple and quadruple zeta).

(2) The use of double zeta basis set could lead to some

mistakes in the frequency assignments. First, the double zeta

basis set, Aug-cc-pvDZ, reverses the position and IR intensity

of the symmetric libration of the acid and the out of phase

ring stretching of the base: 879.0 cm�1 (73.8 km mol�1)

for the symmetric libration of hydracid, and 867.9 cm�1

(155.0 km mol�1) for the out of phase ring stretching of

oxirane at the MP2 level and, respectively, 867.2 cm�1 and

860.3 cm�1 at the CCSD(T) level, whereas the correct ordering

could be obtained using the Aug-cc-pvTZ basis set: 860.4 cm�1

(142.8 km mol�1) and 891.6 cm�1 (63.2 km mol�1) with MP2

and 847.6 cm�1 and 884.7 cm�1 with CCSD(T).

(3) For the bending modes, labelled as od1 and od2, their

MP2 calculated relative positions vary as a function of the

basis set size: with double zeta basis set, od1 is higher than od2;

with triple zeta basis set, od1 is lower than od2; and they are

nearly degenerate with quadruple zeta basis set. Both double

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Fig. 1 Structural parameters of the complex oxirane–HF.a CCSD(T)/Aug-cc-pvTZ. b MP2/Aug-cc-pvTZ. c MP2/Aug-cc-pvQZ.d MP2/6-311++g(2d,2p) from Ref. 33. e Experimental values from

Ref. 42.


and triple zeta basis sets with the CCSD(T) approach give od1lower than od2. In this case, using a highly correlated method

is necessary to avoid errors in the mode assignments.

(4) In the previous publication33 the vibrational calcula-

tions carried out at MP2/6-311++g(2d,2p) level of theory led

to an inversion of the two libration modes: the symmetric

libration was found to be lower (803 cm�1) than the

asymmetric one (819 cm�1). The current theoretical study

done at the CCSD(T)/Aug-cc-pvTZ level clearly indicates that

the symmetric libration is higher in frequency (847.6 cm�1)

than the asymmetric one (829.3 cm�1).

A comparison between the vibrational frequencies of

oxirane, obtained, for instance, at the MP2/Aug-cc-pvQZ

level, reveals that they are nearly unperturbed by the

formation of the hydrogen-bonded complex with a maximum

shift around 25 cm�1 for stretching modes. Inversely, the

stretching frequency of hydracid is strongly affected upon

formation of hydrogen bonds with a harmonic frequency red

shift of about 573 cm�1.

Anharmonic frequencies as well as diagonal and off-

diagonal coupling constants of the acid stretching and inter-

molecular modes calculated at MP2/Aug-cc-pvTZ are

gathered with our experimental values in Table 2. An estima-

tion of CCSD(T)/Aug-cc-pvTZ anharmonic frequencies is

proposed, assuming that diagonal and off-diagonal anharmonic

constants do not differ from the MP2 ones. In this approxima-

tion, CCSD(T) anharmonic frequencies can be written as

follows: uCCSD(T)i = oCCSD(T)

i + (uMP2i � oMP2

i ). The validity

of this approximation and comparison with experimental data

will be discussed in the last part of this paper.

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Table 1 Vibrational frequencies of the oxirane–HF complex: harmonic frequencies (cm�1) at MP2 and CCSD(T) level, as function of the basisset. (Intensities are reported in parentheses, in km mol�1)

MethodMP2 CCSDT

Basis set Aug-cc-pvDZ Aug-cc-pvTZAug-cc-pvQZ

Aug-cc-pvDZAug-cc-pvTZ

Vibrational modes Complex Complex Complex Monomer Complex Complex Monomer

Symmetric bend xd1 98.2 (9.8) 84.9 (8.9) 85.7 (8.7) — 100.9 84.5 —Asymmetric bend xd2 97.4 (0.9) 86.8 (0.8) 85.6 (0.7) — 101.9 88.2 —Intermolecular stretch xr 280.6 (29.3) 275.9 (29.0) 272.6 (28.4) — 278.3 272.2 —B2 CH2 rock 813.5 (17.1) 820.9 (32.5) 821.2 (49.3) 825.4 (0.3) 806.4 811.2 813.6B1 antisym. ring stretch. 788.2 (8.3) 825.2 (3.2) 828.3 (17.9) 852.1 (8.3) 778.8 817.6 839.8Asym. libration xl2 842.1 (76.4) 839.5 (80.9) 832.9 (67.7) — 832.3 829.3 —Sym. libration xl1 879.0 (73.8) 860.4 (142.8) 854.5 (127.3) — 867.2 847.6 —A1 out of phase ring stretch. 867.9 (155.0) 891.6 (63.2) 894.6 (67.0) 903.4 (69.1) 860.3 884.7 893.1A2 CH2 twist 1040.2 (0.1) 1061.7 (0.0) 1065.3 (0.0) 1057.8 (0.0) 1035.8 1057.6 1045.7A1 CH2 wagg. 1138.6 (1.3) 1153.3 (1.0) 1154.1 (1.0) 1150.5 (0.4) 1133.2 1151.0 1150.5B2 CH2 twist 1156.4 (5.7) 1178.9 (5.8) 1181.8 (5.7) 1173.5 (3.7) 1153.6 1176.4 1159.4B1 CH2 wagg. 1160.4 (0.4) 1179.2 (0.5) 1182.6 (0.5) 1168.4 (0.3) 1154.7 1176.2 1165.4A2 CH2 rock 1177.1 (0.2) 1188.9 (0.1)) 1193.8 (0.1) 1183.4 (0.0) 1168.2 1181.3 1171.1A1 in phase ring stretch. 1294.6 (10.7) 1306.9 (13.1) 1310.0 (13.6) 1309.8 (12.0) 1277.2 1293.2 1293.8B1 CH2 scissor. 1495.3 (0.9) 1513.4 (1.3) 1513.2 (1.4) 1515.1 (0.2) 1484.9 1505.0 1505.9A1 CH2 scissor. 1529.2 (2.2) 1544.6 (2.4) 1544.0 (2.3) 1547.6 (1.7) 1521.0 1537.5 1541.7B1 CH stretch. 3166.5 (10.3) 3165.4 (8.6) 3168.7 (8.5) 3151.4 (22.8) 3122.6 3126.3 3107.6A1 CH stretch. 3173.1 (15.0) 3171.7 (13.1) 3174.2 (12.8) 3157.8 (13.8) 3130.3 3133.5 3115.2A2 CH stretch. 3277.3 (0.3) 3270.3 (0.3) 3275.3 (0.3) 3250.1 (0.0) 3224.9 3222.2 3195.4B2 CH stretch. 3290.8 (5.9) 3283.1 (4.4) 3287.6 (4.3) 3263.4 (22.4) 3238.7 3235.5 3210.0Acid stretch xS 3479.7 (1129.6) 3542.9 (1151.7) 3564.9 (1118.3) 4137.4 (122.46) 3539. 5 3601.6 4126.0

Table 2 Vibrational properties of oxirane–HF and oxirane–DF complexes. All theoretical results have been computed with the Aug-cc-pvTZbasis set. Experimental results are reported in brackets. All data are expressed in cm�1

Vibrational mode

Anharmonic frequencies Anharmonic coupling constant (MP2/Aug-cc-pvTZ)

MP2 CCSD(T)a Experimental S l1 l2 s d1 d2

Oxirane–HF S 3369.0 3427.7 [3449.9] 173.5 — — — — —l1 780.8 768.0 [719.0] �115.4 35.9 — — — —l2 762.1 752.0 [714.0] �127.0 42.6 42.5 — — —s 246.8 243.1 [238.0] �34.2 [�32.2] 24.0 23.6 6.3 [6.3] — —d1 78.0 77.8 [67.5] �14.9 [�13.8] 10.1 [10.2] 7.6 [9.0] 5.4 [4.25] 0.5 [0.3] —d2 82.6 84.3 [69.0] �15.7 [�14.0] 9.3 [9.8] 7.4 [8.0] 5.9 [4.75] �0.9 0.5 [0.3]

Oxirane–DF S 2488.3 2530.5 [2547.2] 89.9 — — — — —l1 563.4 553.9 [534.6] �68.4 24.7 — — — —l2 558.6 551.1 [531.9] �65.5 25.6 21.8 — — —s 245.1 241.5 [237.3] �23.9 [�21.0] 20.4 17.6 6.1 [6.2] — —d1 84.5 84.2 — �10.7 [�9.5] 7.0 [6.4] 5.2 [6.1] 5.3 [4.2] 0.8 [0.8] —d2 86.6 88.4 — �11.1 [�10.0] 7.1 [8.0] 5.2 [6.9] 5.8 [4.7] �0.9 0.7 [0.5]

a Anharmonic frequencies at CCSD(T) level estimated as: uCCSD(T)i = oCCSD(T)

i + (uMP2i � oMP2

i ).


III.2 Cooled cell and molecular beam data

a The nr band region. Fig. 2 and 3 display cooled cell

spectra at 253 K recorded in the ns stretching hydrogen bond

region. The two spectra in Fig. 2 have been recorded at

instrumental resolutions D~nFWHM of 0.5 cm�1 (a) and

0.1 cm�1 (b), respectively, and for a ratio of 28/2/30 for the

ternary mixture HF/DF/(CH2)2O. Taking account of the high

HF/DF ratio, we expect to observe only the 1 : 1 (CH2)2O–HF

complex. The use of a better resolution than 0.5 cm�1 partially

resolves some overlapping vibrational features. Due to the

small quantity of DF synthesized (about 1 mol h�1), switching

from pure HF/(CH2)2O to DF/(CH2)2O dilutions could not be

obtained even though several passivation cycles of the cell

were made. The cell spectrum in Fig. 3a recorded at 0.1 cm�1

resolution is obtained for HF/DF/(CH2)2O = 10/20/30. It is

composed of features due both to HF and DF bonded to

(CH2)2O. In agreement with classical mechanics rules, a very

small difference is observed between the O� � �H and O� � �Dstretching hydrogen bond frequencies. In this case overlapping

structures of both contributions are observed and

rovibrational structures of (CH2)2O–HF from the mixed nsHF/DF cell spectrum should be removed. Pure ns spectrum of

(CH2)2O–DF (Fig. 3b) is obtained by subtracting a fraction of

the ns spectrum of (CH2)2O–HF (Fig. 2b) from the mixed nsspectrum. Both cell spectra have been recorded at a total

pressure as high as 60 mbar to get a sufficient dimer absorption

signal. Collisional broadening is expected to be not negligible

at such pressures (for example, self-broadened half-widths gselfas high as 0.73 cm�1 atm�1 have been measured for HF41).

Consequently, an effective homogeneous linewidth gP fixed to

0.2 cm�1 (with an uncertainty of �0.1 cm�1) is introduced to

take into account this effect. The labeling of the observed

absorptions is defined in the same manner as for the previous

analysis of the ns spectrum.33 Capital letters designate different

groups of transitions: (F) for one-quantum transitions vinter =

0- vinter = 1 and (H) for vinter = n- vinter = n+ 1 (n Z 1).

An index, d1 and d2 for bendings, s for stretching, l1 and l2 for

librations which specify the nature of ninter is added to (F) or

(H). The subscript i equal to (0,. . .,vd) refers to the total

bending quantum number vd = vd1 + vd2 involving both

bending modes in hot band sequences. Finally, the labels P,

Q and R correspond to the branches of a rovibrational

transition. The validity of the assignments will be justified in

detail in section III.

The ns spectrum (Fig. 2) is characterized by a series of nine

features Fs(i) spaced by about 4.7 cm�1. The observation of

several narrow substructures in this cell spectrum has to be

linked to previous ns studies of (CH2)2S–HF32 and –DF31 for

which resolved rovibrational branches have been identified

even at near room temperature. The characteristic band

shaping of this hot band sequence suggests a reverse sign of

both cross anharmonicities and rovibrational coupling

constants with respect to the ns band. Starting from the

Fs(0) absorption at 243.6 cm�1 (FWHM E 0.5 cm�1) two

submaxima are then observed within Fs(1) (at 238.7 and

237.9 cm�1) and Fs(2) (at 233.8 and 232.5 cm�1). On these

grounds we attempt to put together submaxima separated by

about 6 cm�1 considering that they respectively belong to R

and Q branches of a same transition. In the following, the

doublets 243.6–237.9 cm�1 and 238.7–232.5 cm�1 will be

associated respectively with the R and Q branches of Fs(0)and Fs(1). For i > 1 the Fs(i) sequence progressively

broadens to 212 cm�1 except for two narrow submaxima at

230.3 and 224.6 cm�1 separated by about the same R � Q

spacing. This doublet, red shifted from 13.3 cm�1 with respect

to Fs(0), could belong to the first member Hs(0) of a second

progression noted Hs(i). The ns spectrum of (CH2)2O–DF

(Fig. 3b) has a similar pattern to the spectrum of that of its

hydrogenated homologue: a Fs(i) absorption with the

doublets 242.7–237.1 cm�1 for Fs(0) and 237.9–231.9 cm�1

for Fs(1), followed by Hs(0) red shifted from 12.8 cm�1 with

respect to Fs(0).

b The nl band region. Fig. 4a displays our best jet spectrumof the nl bands of (CH2)2O–HF recorded at 0.5 cm�1 resolu-

tion with a ternary mixture HF/(CH2)2O/Ar adjusted to

maximize the signal of the 1 : 1 complex. The signal-to-noise

ratio of this spectrum makes it possible only to identify the

maximum of one band contour around 716.7 cm�1.

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Fig. 2 FTIR cell spectrum of the ns stretching band of (CH2)2O–HF,

(a) at 0.5 cm�1 resolution (b) at 0.1 cm�1 resolution (c) our best

simulated spectrum. Rotational lines of HF and DF are observed in

this region. The features marked by a star correspond to the rotational

lines of H2O.

Fig. 3 FTIR cell spectrum of the ns stretching band of (CH2)2O–DF

recorded at 0.1 cm�1 resolution:Q4 (a) with HF/DF/(CH2)2O = 1/2/3,

(b) after subtracting the contribution of the (CH2)2O–HF spectrum,

(c) our best simulated spectrum. The features marked by a star

correspond to the rotational lines of H2O.


Fig. 4b displays the 293 K cell spectrum of the nl bandsrecorded at 0.5 cm�1 resolution. The spectral width of the

features observed practically does not change when the

resolution is increased to 0.2 cm�1. The nl spectrum displays

a main band absorption spread over about 100 cm�1, well

structured on its high frequency side between 725

and 670 cm�1 (Mi = 0,3 will designate hereafter the first

maxima observed at 720.6, 718.3, 716.7 and 715.5 cm�1,

respectively) and progressively blurred out on the low

frequency tail. Two characteristic patterns are expected to

be observed in such a spectrum: (i) a resolved progression

originating from thermally occupied low lying levels of nd1 andnd2 bending modes provided that the off-diagonal coupling

constants exceed the width of rotational contours, (ii) a

complete overlap between both libration bands because

the frequency difference between nl1 and nl2 librations of

H(D)F bonded to oxirane should not exceed some tens

of cm�1. The nl band pattern of (CH2)2O–DF (Fig. 5a)

resembles the HF one.

III.3 Band assignments from FTIR data

Preliminary assignments of the intermolecular ns and nl overallband contours of (CH2)2O–HF and –DF are based on

previous analyses of the ns band for several hydrogen bonded

heterodimers as well as on the theoretical prediction of

rovibrational parameters.

In the ns band region, the RQ doublet of Fs(0) is assigned to

R and Q rotational branches of the ns fundamental transition

(band center: 237.9 cm�1). By analogy with the coupling

scheme identified within the ns band, Fs(i) components likely

correspond to a double hot band sequence involving nd1 andnd2 with similar values of xsd1 and nsd2 (4.25 and 4.75 cm�1,

respectively). The fundamental transition Fs(0) is observed at

the highest frequency of the ns hot band sequence while the

asymmetry of the rotational band contour makes prominent

R and Q branches appear at near room temperature, contra-

dictory to the hot band sequences involving ns. Hs(0) is

tentatively assigned to the overtone vs = 1 - vs = 2 which

would constitute the starting point of a second progression

involving the bending modes but with lesser intensity

(about a ratio of 1/4 with respect to Fs following the

Boltzmann law).

In the nl bands region, spectral congestion is more

important and we are forced to make some assumptions:

due to the positive sign of off-diagonal anharmonicities related

to inter-inter couplings (cf. section III.5), it is expected that the

band contour of intermolecular transitions displays a strong

asymmetry on the R branch side which becomes the most

intense feature of the transition. The component observed in

jet at 716.7 cm�1 as well as the most intense one at 718.3 cm�1

(noted M1) observed in cell could thus correspond to the R

branch of the same libration mode, the 1.6 cm�1 frequency

difference coming from the temperature-dependent blueshift

of the R branch. With the same arguments, the submaximum

M0 at 720.6 cm�1 could be assigned to the R branch of the

second libration mode.

In summary, we proposed the following scenario for the nlbands simulation: two librations separated by a few wave-

numbers with rotational band contours characterized by

resolved R and Q branches and R � Q splittings of about

3–4 cm�1. For each libration hot sequences involving the

participation of nd1 and nd2 bending modes are introduced in

the simulation. As for the H(D)–F (ns) and O� � �H(D) (ns)stretching modes of the same complex, we expect to observe

here slightly different nld values which results in the broadening

of Fl(i) states due to the presence of (vd + 1) nearby states

whose width varies as vd(xld1 � xld2).

III.4 Band contour simulations

The validation of the proposed assignments for

(CH2)2O–H(D)F depends on the good reproduction of the

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Fig. 4 FTIR spectrum of the nl1 and nl2 libration bands of

(CH2)2O–HF, (a) in jet at 1 cm�1 resolution and (b) in cell at

0.5 cm�1 resolution. For each libration mode, hot band sequences

involving nd1 and nd2 are assigned using the sum (vd1 + vd2). In the case

of nl1, transitions with vd1 + vd2 = n (n = 1–5) are very close to each

other and only one number n is reported. In the case of nl2, thesetransitions are more spaced and two numbers of n are reported which

correspond to the lowest and highest frequencies of the cluster of

transitions (vd1 + vd2). The band marked by a star corresponds to the

n2 band of CO2. (c) Our best simulated spectrum.

Fig. 5 FTIR cell spectrum of the nl1 and nd2 libration bands of

(CH2)2O–DF at 0.1 cm�1 resolution (a) and our best simulated

spectrum (b). The same convention as for (CH2)2O–HF has been used

for the assignments of hot band sequences involving nd1 and nd2. Forboth librations, two numbers of n are reported which correspond

to the lowest and highest frequencies of the cluster of transitions

(vd1 + vd2). The band marked by a star corresponds to an impurity

present in the DF spectrum.


three intermolecular bands ns, nl1 and nl2 from our band

contour software enabling the simulation of multiple hot band

progressions in asymmetric rotors, already used in previous

studies.31–35 Several parameters are fixed before starting the

simulation: (i) the ground-state rotational constants obtained

in microwave experiments by Legon et al.,42,43 (ii) the band

hybridization computed from the projection of the dipole

moment related at each normal coordinate (s, l1, l2) onto the

molecular inertial axes, (iii) the cell temperature, (iv) in

addition to the fixed value of gP related to collisional broad-

ening effects, the instrumental resolution D~nFWHM and the

shape of the response function (Happ-Genzel in the present

case) entering the final convolution of the computed spectrum.

At around 300 K, the fundamental band is likely to overlap

with hot transitions. Consequently the determination of

reliable rovibrational coupling constants aXi (with X = A, B,

C and i = s, l1, l2) is based on the delicate deconvolution of

rovibrational structures within cell-FTIR spectra. Firstly, the

fundamental band is reproduced by adjustment of aXi and

eventually of an additional homogeneous linewidth g.Secondly, on the ground of ab initio anharmonic intermole-

cular frequencies and off-diagonal anharmonicities xij hot

band sequences involving bending modes are introduced by

progressively increasing the quantum numbers vd1 and vd2 and

including the corresponding transitions. The first overtone

vs = 1 - 2 and its associated hot sequences are lastly

introduced in the simulation of the ns band in order to

reproduce several missing components while the fundamental

band alone is only considered.

Fig. 2c and 4c display our best simulations obtained

for the ns and nl bands of (CH2)2O–HF. Similar band

patterns are observed for (CH2)2O–DF and lead to

synthetic spectra displayed in Fig. 3c and 5b. The good

agreement between experimental and calculated spectra lends

confidence to the set of molecular parameters reported in

Table 3.

III.5 Discussion

a Rovibrational parameters. The band contour analysis of

a series of cell-FTIR spectra of oxirane bonded to fluoride

hydrogen and deuterium recorded in the 50–750 cm�1 range

enabled the derivation of several rovibrational parameters

involving intermolecular motions. Rovibrational coupling

constants aXi , anharmonic constants xii and xij and anharmonic

frequencies ni could be extracted for the intermolecular modes

ns, nl1 and nl2 of (CH2)2O–HF and –DF. For the lowest

frequency bending modes, nd1 and nd2, very low intensities

calculated at about 9 and 1 km mol�1, respectively (Table 1),

make their detection out Q5of range with our cell device. Several

general tendencies related to intermolecular dynamics within

hydrogen bonded complexes emerge from the spectral

analysis:

(i) Several inter–inter couplings between ns, nl1, nd2 and the

lowest frequency bending modes nd1 and nd2 have been deter-

mined (xij/ni E 1.2% for nl and 1.8% for ns) from the red

shifted progressions observed in the 250–300 K range. The

coupling picture is different from the blue-shifted progressions

previously observed within the ns band:33 in that case the sign

of cross anharmonicities was found to be negative because of

strong couplings between the intramolecular state vs = 1 and

intermolecular motions, which implies a stiffening of

(CH2)2O–H(D)F upon stretching H(D)F (ns) excitation.

Inversely when intermolecular modes such as ns, nl1 and nl2are excited, positive values of xid1 and xid2with i = s, l1, l2 aremeasured which results in a decrease of intermolecular

bending frequencies consistent with a weakening of the

hydrogen bond. Similar conclusions have been obtained by

Nelander et al. with HCl containing HCN26 and CO27 dimers:

the simultaneous decrease of the rotational constant B with

the increase of distortion constant DJ is interpreted as being

due to the excitation of HCl libration which destabilized the

hydrogen bond by almost 20%.

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Table 3 Molecular parameters (cm�1) of oxirane–HF and –DF derived from the band contour analysis of cell-FTIR spectra of intermolecularmodes. For each complex the left column reports previous results obtained in the mid-infrared range from jet- and cell-FTIR spectra of the ns band.Numbers in parentheses indicate estimated uncertainties in units of the last digit

(CH2)2O–HF (CH2)2O–DF

Mid-infrared i = s Far-infrared i = l1, l2, s Mid-infrared i = s Far-infrared i = l1, l2, s

ns 3449.9(2) — 2547.2(2) —nd1 67.5(20) — — —nd2 69.0(20) — — —ns 240.6(20) 238.0(1) — 237.3(1)nl1 — 719.0(1) — 534.6(1)nl2 — 714.0(1) — 531.9(1)xsd1 �13.8(2) — �9.5(2) —xsd2 �14.0(2) — �10.0(2) —xss �32.2(2) — �21.0(2) —xl1d1 [xl1d2] — 9.8[10.2](1) — 6.4[8.0](1)xl2d1 [xl2d2] — 8.0[9.0](1) — 6.1[6.9](1)xd1d1 0.3(2) — 0.5(2) —xd2d2 0.3(2) — 0.8(2) —xsd1 4.7(5) 4.25(10) — 4.2(1)xsd2 5.2(5) 4.75(10) — 4.7(1)xss 7.1(5) 6.3(1) — 6.2(1)g 3.3(1) E0 0.7(1) E0aAi 0.009(2) 0.001(2), 0.000(2), 0.000(2) 0.015(3) 0.000(2), 0.001(2), 0.000(2)

aBi + aCi �0.010(1) 0.016(4), 0.006(4), 0.005(4) �0.0095(5) 0.010(4), 0.012(4), 0.005(4)


(ii) Positive values of aXi extracted from our simulations

(about 3% for aXi /X0) evidenced a small decrease of the

rotational constants in the different excited states probed by

FTIR spectroscopy. This variation suggests a slight elongation

of the complex upon the three intermolecular excitations in

agreement with the conclusions derived in (i).

(iii) The reliability of the far-infrared data has to be

questioned by comparing direct observations of inter-

molecular vibrations with mid-infrared results obtained from

|0,vinter,i,. . .i- |vintra,vinter,i,. . .i or |0,0,. . .i- |vintra,vinter,i,. . .itransitions (Table 3) as well as anharmonic ab initio calcula-

tions (Table 2).

Four vibrational parameters related to the stretching

hydrogen bond mode, namely ns and xsj (j = s, d1, d2), havebeen derived via FIR and MIR experiments. Both sets of

values compare outstandingly well between them (Table 3),

with standard deviations smaller than 1% and 12%, for ns andxsj respectively.

As shown in Table 2, calculated coupling constants xii and

xij agree well with experimental ones, with a root mean squares

deviation of 1.1 cm�1 for oxirane–HF and 1.3 cm�1 for

oxirane–DF. Off-diagonal anharmonicities are found to

always be higher than the experimental ones for stretching

modes but lower for librations and bendings.

Since calculation of the anharmonic frequencies are not

always available using the CCSD(T) approach, we suggested

(section III.1.b) a route to estimate the anharmonic

frequencies at the CCSD(T) level using the MP2 anharmonic

coupling constants. With these latter constants being in

excellent agreement with the experimental values, we were

able to obtain a CCSD(T) estimation of the anharmonic

frequencies closer to experimental frequencies than the MP2 ones.

For both complexes all calculated intermolecular

frequencies are higher than experimental ones while theoreti-

cal acid stretching frequencies are lower than the experimental

ones. This deviation is consistent with an overestimation of the

hydrogen bond strength involving, at the same time,

higher intermolecular frequencies and lower acid stretching

frequencies. In comparison with experimental frequencies,

calculated stretching modes (ns and ns) systematically agree

better than bending and libration modes. Deviations amount

to respectively �22 cm�1 (�0.6%) for ns, 5 cm�1 (2.1%) for ns,

49 cm�1 (6.8%) for nl and 10 cm�1 (15.6%) for nd. Thesediscrepancies could be explained by the use of rectilinear

normal coordinates, which are not appropriate for studying

such large amplitude intermolecular modes comparable to

rotation motions of the monomers.

b Dynamic parameters. Our previous studies of medium

strength hydrogen bonded complexes had evidenced large

values of the effective homogeneous linewidth g when the high

frequency donor stretch mode is excited.29 The broadening

parameter g generally contains reliable information on the

predissociation dynamics, which can be nevertheless masked

by other mechanisms which take place at high excitation

energies. In the case of oxirane, excitation energies of the

donor stretch mode are 3450 and 2547 cm�1, respectively, for

HF and DF, which falls above the D0 dissociation limit

evaluated in the previous paragraph. However, the evident

correlation between g values fitted from band contour simula-

tions to 3.3 and 0.7 cm�1 and the vibrational density of states

(rvib) estimated to 220 and 50 states per cm�1 at relevant

energies ns(HF) and ns(DF) has been interpreted as being due

to a major contribution of IVR. Consequently, only lower

bounds on the predissociation lifetime for the vs = 1 state

could be provided, namely 1.5 ps for HF and 7 ps for DF.33 In

the present study, only a small Lorentzian homogeneous

contribution (fixed to 0.2(1) cm�1) attributed to collisional

broadening should be introduced to reproduce correctly the

broadening of intermolecular hot band sequences in Fourier

transform cell spectra of (CH2)2O–H(D)F dimers. This result

correlates well with the previsible absence of any additional

homogeneous contribution: excitation energies used for

this intermolecular study largely fall below the dissociation

threshold and the vibrational density of states is about

one per cm�1, which clearly eliminates both predissociation

and IVR contributions.

IV. Concluding remarks

In summary, a combined Fourier transform far-infrared

spectroscopy and ab initio study on (CH2)2O–HF and DF

has brought reliable information in the field of weak inter-

molecular interactions within hydrogen bonded complexes:

(i) an extended set of spectroscopic parameters, including

excited-state rovibrational constants, anharmonic inter-

intermolecular and inter-intramolecular coupling constants

and intermolecular band centers, could be derived from the

direct excitation of intermolecular states in the far-infrared

region; (ii) the reliability of these experimental data is fully

validated by an excellent agreement obtained from ab initio

calculations using highly correlated methods with extended

basis sets. It has been clearly evidenced that very high level

theory must be used at anharmonic level to correctly

reproduce the rovibrational properties of such hydrogen

bonded dimers; (iii) this latter remark is also intended for

the dissociation energy of both complexes between oxirane

and HF or DF which has been extrapolated at the CCSD(T)/

Aug-cc-pvQZ level—using an insufficient level of theory leads

to an overestimation of DCP0 .

Acknowledgements

The authors thank the SMART federation for the funds

allocated to computational resources.

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Intermolecular vibrations of (CH2)2O–HF and –DF hydrogen bonded complexes investigated by Fourier transform infrared spectroscopy and ab initio calculations

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